Radius of convergence in lattice QCD at finite $\mu_B$ with rooted staggered fermions

Understand

In typical statistical mechanical systems the grand canonical partition function at finite volume is proportional to a polynomial of the fugacity $e^{\mu/T}$.

• The zero of this Lee-Yang polynomial closest to the origin determines the radius of convergence of the Taylor expansion of the pressure around $\mu=0$.
• The computationally cheapest formulation of lattice QCD, rooted staggered fermions, with the usual definition of the rooted determinant, does not admit such a Lee-Yang polynomial.
• We argue that the radius of convergence is then bounded by the spectral gap of the reduced matrix of the unrooted staggered operator.